Problem: Rewrite as a simplified fraction. ${3.6\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 361.1111...\\ 10x &= 36.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 325}$ ${x = \dfrac{325}{90}} $ ${x = \dfrac{65}{18}} \text{or} {3 \dfrac{11}{18}}$